module Recursion where
{-
-}

maximum' :: (Ord a) => [a] -> a
maximum' [] = error "empty list"
maximum' [x] = x
maximum' (x:xs) = max x (maximum' xs)


replicate' :: Int -> a -> [a]
replicate' n x
   | n <= 0 = []
   | otherwise = x : replicate' (n-1) x
   

take' :: (Num i, Ord i) => i -> [a] -> [a]
take' n _
   | n <= 0 = []
take' _ [] = []
take' n (x:xs) = x : take' (n-1) xs


reverse' :: [a] -> [a]
reverse' [] = []
reverse' (x:xs) = reverse' xs ++ [x]


repeat' :: a -> [a]
repeat' x = x:repeat' x

zip' :: [a] -> [b] -> [(a,b)]
zip' _ [] = []
zip' [] _ = []
zip' (x:xs) (y:ys) = (x,y):zip' xs ys

elem' :: (Eq a) => a -> [a] -> Bool
elem' a [] = False
elem' a (x:xs)
   | a == x = True
   | otherwise = a `elem` xs
   
   
quicksort :: (Ord a) => [a] -> [a]
quicksort [] = []
quicksort (x:xs) = 
   let smallerOrEqual = [a | a <- xs, a <= x]
       larger = [a | a <- xs, a > x]
	in quicksort smallerOrEqual ++ [x] ++ quicksort larger